Аннотация:
We have discovered a new first integral in the problem of motion of a dynamically symmetric ball, subject to gravity, on the surface of a paraboloid. Using this integral, we have obtained conditions for stability (in the Lyapunov sense) of steady rotations of the ball at the upmost, downmost and saddle point.
Образец цитирования:
A. V. Borisov, A. A. Kilin, I. S. Mamaev, “Stability of Steady Rotations in the Nonholonomic Routh Problem”, Regul. Chaotic Dyn., 13:4 (2008), 239–249
\RBibitem{BorKilMam08}
\by A.~V.~Borisov, A.~A.~Kilin, I.~S.~Mamaev
\paper Stability of Steady Rotations in the Nonholonomic Routh Problem
\jour Regul. Chaotic Dyn.
\yr 2008
\vol 13
\issue 4
\pages 239--249
\mathnet{http://mi.mathnet.ru/rcd574}
\crossref{https://doi.org/10.1134/S1560354708040011}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2456920}
\zmath{https://zbmath.org/?q=an:1229.70021}
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd574
https://www.mathnet.ru/rus/rcd/v13/i4/p239
Эта публикация цитируется в следующих 8 статьяx:
Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “A Parabolic Chaplygin Pendulum and a Paul Trap: Nonintegrability, Stability, and Boundedness”, Regul. Chaotic Dyn., 24:3 (2019), 329–352
Alexey V. Borisov, Alexander A. Kilin, Ivan S. Mamaev, “A Nonholonomic Model of the Paul Trap”, Regul. Chaotic Dyn., 23:3 (2018), 339–354
Alexey V. Borisov, Alexey O. Kazakov, Igor R. Sataev, “Spiral Chaos in the Nonholonomic Model of a Chaplygin Top”, Regul. Chaotic Dyn., 21:7-8 (2016), 939–954
Ю. Л. Караваев, А. А. Килин, “Динамика сфероробота с внутренней омниколесной платформой”, Нелинейная динам., 11:1 (2015), 187–204
Yury L. Karavaev, Alexander A. Kilin, “The Dynamics and Control of a Spherical Robot with an Internal Omniwheel Platform”, Regul. Chaotic Dyn., 20:2 (2015), 134–152
François Robert Hogan, James Richard Forbes, “Modeling of spherical robots rolling on generic surfaces”, Multibody Syst Dyn, 35:1 (2015), 91
A.V. Bolsinov, A.V. Borisov, I. S. Mamaev, “Hamiltonization of Nonholonomic Systems in the Neighborhood of Invariant Manifolds”, Regul. Chaotic Dyn., 16:5 (2011), 443–464
А. В. Болсинов, А. В. Борисов, И. С. Мамаев, “Гамильтонизация неголономных систем в окрестности инвариантных многообразий”, Нелинейная динам., 6:4 (2010), 829–854
Цитирование в формате AMSBIB
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